Studies of probe tip materials by atomic force microscopy: a review

• Ke Xu and
• Yuzhe Liu

Beilstein J. Nanotechnol. 2022, 13, 1256–1267, doi:10.3762/bjnano.13.104

• extraction process lead to a columnar growth of the clusters, i.e., a more minor contribution of vdW interactions to the total force. To address these issues, Jiménez-Sánchez et al. subjected a blunt tip to multiple clustering extractions and characterized the extracted tip using F(z) spectra. As shown in

• Figure 1a and Figure 1b, the F(z) curve and the high-resolution NC-AFM image were used as criteria to test the conditions of the constructed nano-tip. It can be seen from the Figure 1 that the tip remains intact, and the atomic and molar periodicity in the images is resolved with high quality. This work

• a macroscopic sample exchange. (a) F(z) curves corresponding to the milestones in the sharpening process. The red curve corresponds to the initial blunt tip. The blue curve, measured in the same Ir/G/Rh(111) sample, shows the decrease of the vdW force after the sharpening with clusters. The black

Local stiffness and work function variations of hexagonal boron nitride on Cu(111)

• Abhishek Grewal,
• Yuqi Wang,
• Matthias Münks,
• Klaus Kern and
• Markus Ternes

Beilstein J. Nanotechnol. 2021, 12, 559–565, doi:10.3762/bjnano.12.46

• measurement techniques agree well in their qualitative results as it is evident from the ΔΦ maps (see Figure 3c,e). Stiffness Probing the force perpendicular to the substrate, F⟂, at varying tip–sample separations z, the effective stiffness of a nanostructure can be evaluated by comparing the F⟂(z) behaviour

Quantitative determination of the interaction potential between two surfaces using frequency-modulated atomic force microscopy

• Nicholas Chan,
• Carrie Lin,
• Tevis Jacobs,
• Robert W. Carpick and
• Philip Egberts

Beilstein J. Nanotechnol. 2020, 11, 729–739, doi:10.3762/bjnano.11.60

• interaction forces and relative tip–sample separation displacement, referred to as piezoactuator displacement henceforth. This relation will be referred to as F(z) curves for the remainder of the manuscript. Experimental F(z) curves were then compared with theoretical LJ F(z) curves. These LJ F(z) curves were

• matching these F(z) curves to a set of LJ F(z) curves generated for the specific tip apex shape, as described in the following section. Determination of work and range of adhesion using in situ TEM adhesive experiments The method that will be discussed to determine LJ parameters from dynamic FM-AFM

• method of disks, whereby the tip is approximated as a stack of thin axisymmetric disks normal to the flat diamond surface (Figure 1b). Using these additional data, an LJ F(z) curve was generated by assuming that the silicon oxide–carbon interaction is described by the 6-12 LJ pair potential. This was

Imaging the surface potential at the steps on the rutile TiO₂(110) surface by Kelvin probe force microscopy

• Masato Miyazaki,
• Huan Fei Wen,
• Quanzhen Zhang,
• Yuuki Adachi,
• Jan Brndiar,
• Ivan Štich,
• Yan Jun Li and
• Yasuhiro Sugawara

Beilstein J. Nanotechnol. 2019, 10, 1228–1236, doi:10.3762/bjnano.10.122

• ) Topographic image and (b) height profile. (c) CPD image and (d) CPD line profile. Line profiles were taken along the black line in (a) and (c). (e) Short-range force curve measured on the terrace. (f) Z–X KPFM data obtained along the black line in (a). The measured z-region corresponds to the blue square in

Electro-optical interfacial effects on a graphene/π-conjugated organic semiconductor hybrid system

• Karolline A. S. Araujo,
• Luiz A. Cury,
• Matheus J. S. Matos,
• Thales F. D. Fernandes,
• Luiz G. Cançado and
• Bernardo R. A. Neves

Beilstein J. Nanotechnol. 2018, 9, 963–974, doi:10.3762/bjnano.9.90

• modeled by where, ω0 and k are the cantilever’s resonant frequency and spring constant, respectively, C´´(z) is the second derivative of the tip–sample capacitance C(z), Vtip is the applied bias, Φ is the tip–sample surface potential difference, and f´(z) is the first derivative of the electric force

Electrical properties of a liquid crystal dispersed in an electrospun cellulose acetate network

• Doina Manaila Maximean,
• Octavian Danila,
• Pedro L. Almeida and
• Constantin Paul Ganea

Beilstein J. Nanotechnol. 2018, 9, 155–163, doi:10.3762/bjnano.9.18

• impedance shift to higher frequencies (Figure 8). The Cole–Cole [32] diagrams, Z″ = f(Z′), are presented in Figure 9. The semicircular shapes of the diagrams allow for modelling the raw data with a theoretical three-element electric circuit model, consisting of a series resistance, a parallel resistance and

Modelling of ‘sub-atomic’ contrast resulting from back-bonding on Si(111)-7×7

• Adam Sweetman,
• Samuel P. Jarvis and
• Mohammad A. Rashid

Beilstein J. Nanotechnol. 2016, 7, 937–945, doi:10.3762/bjnano.7.85

• position of single F(z) and Δf(z) curves are marked on the xy images, and the heights of each image is marked on the graphs with the corresponding Greek letter. The Δf contrast and evolution in z is qualitatively similar for the force and 0.5 nm oscillation amplitude simulations. The simulations with an

A simple and efficient quasi 3-dimensional viscoelastic model and software for simulation of tapping-mode atomic force microscopy

• Santiago D. Solares

Beilstein J. Nanotechnol. 2015, 6, 2233–2241, doi:10.3762/bjnano.6.229

• position but in terms of both position and velocity (that is, the force is expressed as instead of simply F(z)). This enhanced representation may make it possible to invert the AFM observables to obtain viscoelastic model parameters. At this time this approach is still limited by experimental capabilities

Large-voltage behavior of charge transport characteristics in nanosystems with weak electron–vibration coupling

• Tomáš Novotný and
• Wolfgang Belzig

Beilstein J. Nanotechnol. 2015, 6, 1853–1859, doi:10.3762/bjnano.6.188

• characteristic curves reads with the roots and has the solution with an integration constant C labeling various characteristic curves. The variation of the function F(z,t;λ) along each separate characteristic curve is ruled by the equation yielding with Ω an arbitrary function of the integration constant C. It

• implies the initial condition for F(z,t = 0;λ) = 1 and consequently Putting things together we finally arrive at For λ = 0 we recover the solution (VI.6.4) of [29] with r = m = 0, g = 1, a = γ↓, b = γ↑. The large time asymptotics of Equation 18 is which leads to the sought-for expression for the CGF This

Nano-contact microscopy of supracrystals

• Adam Sweetman,
• Nicolas Goubet,
• Ioannis Lekkas,
• Marie Paule Pileni and
• Philip Moriarty

Beilstein J. Nanotechnol. 2015, 6, 1229–1236, doi:10.3762/bjnano.6.126

• dispersion forces [41]. However, while force–distance measurements of single molecule interactions using this technique are typically highly reproducible [31][33][41][42][43], we observe a very large degree of variation between different F(z) spectra for the nanocrystals. Although the broad trends remain

• . pointed out in their pioneering paper on point-contact microscopy using STM [22]. However, regardless of whether we define the contact point as the tip–sample separation associated with the minimum of the potential energy curve (i.e., where F(z) = 0) or as the point at which the gradient of the force

Multiscale modeling of lithium ion batteries: thermal aspects

• Arnulf Latz and
• Jochen Zausch

Beilstein J. Nanotechnol. 2015, 6, 987–1007, doi:10.3762/bjnano.6.102

• determined by Φ through Equation 10 and not by φ. It is possible to obtain the formulation in Equation 44 and Equation 45 directly from the entropy law by choosing the flux N+ and the electric current j together with the molar density c+ = ρ+/M+ =: c and the free charge density ρF = F(z+c+ + z−c−) as primary

Injection of ligand-free gold and silver nanoparticles into murine embryos does not impact pre-implantation development

• Ulrike Taylor,
• Wiebke Garrels,
• Annette Barchanski,
• Svea Peterson,
• Laszlo Sajti,
• Andrea Lucas-Hahn,
• Lisa Gamrad,
• Ulrich Baulain,
• Sabine Klein,
• Wilfried A. Kues,
• Stephan Barcikowski and
• Detlef Rath

Beilstein J. Nanotechnol. 2014, 5, 677–688, doi:10.3762/bjnano.5.80

• control, (E) 3 days after AuNP injection, (F) z-axis of (E). AuNP appear in red, some of which are exemplarily pointed out with arrows. Representative stereo microscope images of murine blastocysts (A) after silver nanoparticle-injection (10 pL of a 50 µg/mL nanoparticle dispersion, equal to 3300

Uncertainties in forces extracted from non-contact atomic force microscopy measurements by fitting of long-range background forces

• Adam Sweetman and
• Andrew Stannard

Beilstein J. Nanotechnol. 2014, 5, 386–393, doi:10.3762/bjnano.5.45

• extrapolation method. Keywords: background subtraction; DFM; F(z); force; atomic resolution; NC-AFM; Si(111); STM; van der Waals; Introduction Non-contact atomic force microscopy (NC-AFM) is now the tool of choice for surface scientists wishing to investigate interatomic and intermolecular forces on surfaces

Structural development and energy dissipation in simulated silicon apices

• Samuel Paul Jarvis,
• Lev Kantorovich and
• Philip Moriarty

Beilstein J. Nanotechnol. 2013, 4, 941–948, doi:10.3762/bjnano.4.106

• unstable structures can be revealed by a characteristic hysteretic behaviour present in the F(z) curves that were calculated with DFT, which corresponds to a tip-induced dissipation of hundreds of millielectronvolts resulting from reversible structural deformations. Additionally, in order to model the

• affect calculated tip-force F(z) curves and the hysteresis pathways followed by the tip and surface structures [28]. For instance, the bulk-like rear structure of tip apices is almost always aligned parallel to the surface for convenience when designing the tip. There is no reason to expect, however

• , stabilised tip geometries. We find that a tip prone to this behaviour demonstrates enhanced hysteresis in calculated F(z) data, dependent only on deformations within the tip apex, until complex structural rearrangements move the geometry into a more stable state. This suggests that even when varying just a

Towards 4-dimensional atomic force spectroscopy using the spectral inversion method

• Jeffrey C. Williams and
• Santiago D. Solares

Beilstein J. Nanotechnol. 2013, 4, 87–93, doi:10.3762/bjnano.4.10

• method, the user performs a 2-dimensional (2D) scan of the surface to acquire the topography plus a tip–sample force curve, f(z), at every (x,y) pixel, which effectively results in a 3D description of the tip–sample forces, f(x,y,z). The force curves for each sample location are plotted as 2D graphs

Probing three-dimensional surface force fields with atomic resolution: Measurement strategies, limitations, and artifact reduction

• Mehmet Z. Baykara,
• Omur E. Dagdeviren,
• Todd C. Schwendemann,
• Harry Mönig,
• Eric I. Altman and
• Udo D. Schwarz

Beilstein J. Nanotechnol. 2012, 3, 637–650, doi:10.3762/bjnano.3.73

• adjustments can be carried out by comparison with site-specific high-density ∆f(z) calibration curves recorded directly before and/or after the individual layers needed to assemble the actual data array. Alternatively, curves of tunneling current versus distance can serve the same purpose if the tunneling

• ) for most tip–sample distances (Figure 6a). At very close separations, however, the atomically sharp tip apex employed in the simulations experiences a larger attractive force on the site of the minima of the surface potential (the hollow sites). This force contrast flip causes a crossing of the ∆f(z

• fields. Schematic drawings illustrating data-acquisition procedures employed to record the atomic-scale surface force fields Fn(x, y, z) experienced by a probe tip. While the curve-by-curve approach (a) relies on sequential recording of individual ∆f(z) curves at each (x, y) location on the surface that

Theoretical study of the frequency shift in bimodal FM-AFM by fractional calculus

• Elena T. Herruzo and
• Ricardo Garcia

Beilstein J. Nanotechnol. 2012, 3, 198–206, doi:10.3762/bjnano.3.22

• of the force gradient with the semicircle [24]: By using the definition of the Laplace transforms of the force F(z) and its derivative F′(z) By substituting Equation 8 in Equation 6 we have where T′(x) can be expressed in terms of the modified Bessel function of the first kind of order zero I0(x) (T